TTT, flux et champs vectoriel pour la visualisation de matrice OD

Installation de ttt

remotes::install_github("tributetotobler/ttt")
library(ttt)
library(sf)
library(dplyr)

Exercise 1 : un exemple historique, les dollars de Tobler

Lire des données

Importez les données dollars contenues dans le package ttt et regardez leurs structure.

Indices

Utilisez data(dollars) et str(dollars)

Solution

data(dollars)
str(dollars)

List of 3
 $ OD       : int [1:12, 1:12] 2040 602 143 68 150 122 97 31 14 20 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:12] "Boston" "New York" "Philadelphia" "Cleveland" ...
  .. ..$ : chr [1:12] "Boston" "New York" "Philadelphia" "Cleveland" ...
 $ coords   :'data.frame':  12 obs. of  5 variables:
  ..$ V1: logi [1:12] NA NA NA NA NA NA ...
  ..$ V2: num [1:12] 65.4 59.7 59.8 53.2 57.8 ...
  ..$ V3: logi [1:12] NA NA NA NA NA NA ...
  ..$ V4: num [1:12] 37.2 33.3 29.9 27.2 22.6 ...
  ..$ V5: logi [1:12] NA NA NA NA NA NA ...
 $ polygones:Classes 'sf' and 'data.frame': 12 obs. of  2 variables:
  ..$ geom:sfc_POLYGON of length 12; first list element: List of 1
  .. ..$ : num [1:10, 1:2] 64 67 66 66 69 67 65 64 62 64 ...
  .. ..- attr(*, "class")= chr [1:3] "XY" "POLYGON" "sfg"
  ..$ name: chr [1:12] "Boston" "New York" "Philadelphia" "Cleveland" ...
  ..- attr(*, "sf_column")= chr "geom"
  ..- attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA
  .. ..- attr(*, "names")= chr "name"

Vous deviez avoir dans votre environement une liste dollars avec trois champs :

• un champ OD contenant une matrice OD de taille 12 x 12 contenant des flux
• un champ polygones contenant les contours des 12 régions des USA

Observations et prétraitements

Importez les données dollars contenues dans le package ttt et regardez leurs structure.

Solution

delta = rowSums(dollars$OD)-colSums(dollars$OD)
dollars$polygones$delta=delta

Solution

plot(st_geometry(dollars$polygones))
plusmoins(dollars$polygones,"delta")

Solution

pot.dollars = poisson.potential(dollars$polygones,nb_it = 5000)

Building grid
Cleanning borders
Grid is build, it contains 1614 cells
Grid weighting performed
Solving poisson equations
mse: 22.3897897645124
mse: 20.197521032228
mse: 18.6065988326793
mse: 17.4846707417539
mse: 16.4880604660814
mse: 15.7189885653791
mse: 14.9856094686621
mse: 14.3952472203219
mse: 13.81594707792
mse: 13.3351743172512
mse: 12.8590743127507
mse: 12.4533527610829
mse: 12.0518450536298
mse: 11.7012285411363
mse: 11.356253268265
mse: 11.0480427831814
mse: 10.7473199874747
mse: 10.4728568118532
mse: 10.2076082289713
mse: 9.96068579042728
mse: 9.72440835534995
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mse: 0.000431507800770375
mse: 0.000428566237903467
mse: 0.000430687429447143
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mse: 0.00042905507550002
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mse: 0.000428243073811325
mse: 0.00042532694183531
mse: 0.000427433842990641
mse: 0.000424524034132649
mse: 0.00042662737358702
mse: 0.000423723874072547
mse: 0.000425823656181049
mse: 0.000422926452269582
mse: 0.000425022681385831
mse: 0.00042213175937064
mse: 0.000424224439846612
mse: 0.000421339786054448
mse: 0.00042342892224045
mse: 0.000420550523031458
mse: 0.000422636119276452
mse: 0.000419763961043882
mse: 0.000421846021695197
mse: 0.000418980090865558
mse: 0.00042105862026856
mse: 0.000418198903301921
mse: 0.000420273905799919
mse: 0.000417420389189598
mse: 0.000419491869125004
Post-processing

Solution

plot(pot.dollars%>% select(attractivity))

Solution

plot(st_geometry(dollars$polygones))
poisson.flows(pot.dollars)

reproducibility

sessionInfo()

R version 4.1.1 (2021-08-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.3 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

locale:
 [1] LC_CTYPE=fr_FR.UTF-8       LC_NUMERIC=C               LC_TIME=fr_FR.UTF-8       
 [4] LC_COLLATE=fr_FR.UTF-8     LC_MONETARY=fr_FR.UTF-8    LC_MESSAGES=fr_FR.UTF-8   
 [7] LC_PAPER=fr_FR.UTF-8       LC_NAME=C                  LC_ADDRESS=C              
[10] LC_TELEPHONE=C             LC_MEASUREMENT=fr_FR.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ttt_0.1.0   dplyr_1.0.7 sf_1.0-2    knitr_1.35 

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.7         highr_0.9          compiler_4.1.1     pillar_1.6.2      
 [5] unilur_0.4.0.9100  jquerylib_0.1.4    class_7.3-19       tools_4.1.1       
 [9] digest_0.6.28      lattice_0.20-44    evaluate_0.14      lifecycle_1.0.0   
[13] tibble_3.1.3       pkgconfig_2.0.3    rlang_0.4.11       igraph_1.2.6      
[17] Matrix_1.3-4       DBI_1.1.1          yaml_2.2.1         xfun_0.26         
[21] fastmap_1.1.0      e1071_1.7-9        stringr_1.4.0      generics_0.1.0    
[25] vctrs_0.3.8        tidyselect_1.1.1   classInt_0.4-3     grid_4.1.1        
[29] glue_1.4.2         R6_2.5.1           fansi_0.5.0        rmarkdown_2.11    
[33] purrr_0.3.4        magrittr_2.0.1     htmltools_0.5.2    ellipsis_0.3.2    
[37] units_0.7-2        assertthat_0.2.1   KernSmooth_2.23-20 utf8_1.2.2        
[41] stringi_1.7.4      proxy_0.4-26       crayon_1.4.1